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Numerical solution of special two-order boundary-value problems

R. Jalilian|I. Almassi|A. Sephrianazar|H. Jalilian
장전수학회 (Jangjeon Mathematical Society)|2012.01|Advanced Studies in Contemporary Mathematics|제22권 제1호|pp. 75-83

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참고문헌

키워드

Convergence analysisSecond-order ordinary differential equationSingularly-perturbedQuartic spline
주제분류수학

초록

We develop a method for the numerical solution of singularly per-turbed two-point boundary-value problems by using quartic spline at mid knots. The purposed method is fourth-order accurate and ap-plicable to problems both in singular and non-singular cases. The convergence analysis of the method is discussed and numerical results are given to illustrate the effciency of our method.

Abstract

We develop a method for the numerical solution of singularly per-turbed two-point boundary-value problems by using quartic spline at mid knots. The purposed method is fourth-order accurate and ap-plicable to problems both in singular and non-singular cases. The convergence analysis of the method is discussed and numerical results are given to illustrate the effciency of our method.

참고문헌 (17)

  1. CHIN, R. C. Y, "A hybrid asymptotic nite element method for sti two point boundary value problems", SIAM Journal on Scienti c and Statistical Computing, 4, pp.229~243 (1983)
  2. JAIN, M. K., "Numerical solution of sti and convec- tiondi usion equation using adaptive spline function approximation", Applied Mathematical Modeling, 7, pp.57~63 (1983)
  3. MAJER, M. R, "Numerical solution of singularly-perturbed boundary- value problems using a collocation method with tension splines", Progress in Scientific Computing, 5, pp.206~223 (1985), Birkhauser
  4. SURLA, K, "Solving singularly-perturbed boundary- value problems by splines in tension", Journal of Computational and Applied Mathematics, 24, pp.355~363 (1988)
  5. SURLA, K, "A nally of exponen- tial spline dierence scheme, Review of Research, Faculty of Science, Mathematics Series", University of Novi Sad, 19, pp.12~23 (1991)
  6. SURLA, K, "A spline dierence scheme for boundary-value problems with a small parameter, Review of Re- search, Faculty of Science, Mathematics Series", University of Novi Sad, 25, pp.159~166 (1995)
  7. KADALBAJOO, M. K, "Variable-mesh dierence scheme for singularly-perturbed boundary-value problem using splines", Journal of Optimization Theory and Applications, 9, pp.405~416 (1996)
  8. RASHIDINIA, J., "Applications of spline to numerical solution of dier- ential equations", 석사, pp.1990
  9. RASHIDINIA, J, "Variable mesh method for a singular two-point bound- ary value problem", International Journal of Engineering Science, 1, pp.23~33 (2003)
  10. MOHANTY, R. K, "Spline in com- pression method for the numerical solution of singularly perturbed two-point singular boundary-value problems", International Journal of Computer Mathematics, 81, pp.615~627 (2004)
  11. RASHIDINIA, J, "Spline approach to the solution of a singularly-perturbed boundary-value problems", Applied Mathematics and Computation, 189, pp.72~78 (2007)
  12. AZIZ, T, "Quintic spline approach to the solution of a singularly-perturbeb boundary-value problem", Journal of Optimiza- tion Theory Applications, 12, pp.517~527 (2002)
  13. KHAN, A., "Sextic spline solution of singularly- perturbeb boundary-value problems", Applied Mathematics and Com- putation, 181, pp.432~439 (2006)
  14. USMANI, R. A, "The use of quartic splines in the numerical solution of a fourth-order boundary-value problem", Journal of Computational and Applied Mathematics, 44, pp.187~199 (1992)
  15. MILLER, J. J. H, "On the convergence, uniformly in , of di erence schemes for a two-point boundary singular perturbation problem, in: Numerical analysis of singular perturbation problems", pp.467~474 (1979), Academic press
  16. NIIJIMA, K, "On a three-point di erence scheme for a singular per- turbation problem without a rst derivative term I", Mem. Numer. Math, 7, pp.1~10 (1980)
  17. NIIJIMA, K, "On a three-point di erence scheme for a singular per- turbation problem without a rst derivative term II", Mem. Numer. Math, 7, pp.11~27 (1980)

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